The Brauer group of an affine rational surface with a non-rational singularity

JOURNAL OF ALGEBRA

卷:388

Article

Ford, Timothy J.¹  Harmon, Drake M.¹ 

[1] Florida Atlantic Univ, Dept Math, Boca Raton, FL 33431 USA

关键词: Brauer group;    Picard group;    Algebraic surface;    Class group;    Affine algebraic variety;   

DOI  :  10.1016/j.jalgebra.2013.04.022

来源: Elsevier

【 摘 要 】

The object of study is the family of normal affine algebraic surfaces defined by equations of the form z(n) = (y - a(1)x) ... (y - a(n)x)(x - 1). Each surface X in this family is rational and contains a non-rational singularity. Using an explicit resolution of the singularity, many computations involving Well divisors and Azumaya algebras on X are completely carried out. The Picard group and Brauer group are shown to depend in subtle ways on the values a(1),..., a(n). For an odd prime n, and for a general choice of X, the Picard group and the Brauer group are computed. (c) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free